Not signed in (Sign In)

Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

  • Sign in using OpenID

Site Tag Cloud

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nforum nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf sheaves simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).
    • CommentRowNumber1.
    • CommentAuthorRodMcGuire
    • CommentTimeNov 4th 2013

    I’ve added the following definition to power set

    • the slice category Inj/SInj/S, where Inj is the wide subcategory of Set with morphisms restricted to injections. This is similar to the subobject definition but is more unpacked. Inj/SInj/S has objects that are injections to SS and morphisms that are commuting triangles of injections.

    I’ve seen InjInj appear in discussions (as as a simple thing everybody knows) but sometimes there iis confusion about its properties. Could it use its own page?

    (as usual I may be confused/misguided here)

    • CommentRowNumber2.
    • CommentAuthorMike Shulman
    • CommentTimeNov 5th 2013

    I would say feel free to create a page Inj.

    • CommentRowNumber3.
    • CommentAuthorTodd_Trimble
    • CommentTimeNov 5th 2013

    The only thing I’ll say for now is that I’m not convinced InjInj is the best notation. It seems more usual practice to name a category after its objects than after its morphisms; for this reason, instead of InjInj, I might consider Set injSet_{inj}. (Elsewhere we do refer to a category \mathcal{M} who objects are monomorphisms or injections between sets and whose morphisms are commutative squares, so while InjInj is untaken, I’m just slightly leery about it.)

    • CommentRowNumber4.
    • CommentAuthorMike Shulman
    • CommentTimeNov 5th 2013

    Todd, I considered making the same comment. Unfortunately, Set injSet_{inj} is difficult to use as a name for an nLab page… Maybe this should just go on the page injection?

    • CommentRowNumber5.
    • CommentAuthorTodd_Trimble
    • CommentTimeNov 5th 2013

    Yeah, a dedicated section on this category at injection might not be a bad idea. Finite sets and injections is also a category of note that could be written about (semicartesian operads, Schanuel topos, etc.) – or maybe we already have something on this?

    • CommentRowNumber6.
    • CommentAuthorRodMcGuire
    • CommentTimeNov 5th 2013

    I would prefer to have a separate page for InjInj that also describes FinInjFinInj. Of course the page should actually be named something like “category of injections between sets” and various alternative abbreviations of the category names can be given there.

    Having such a page would help find where these categories are used in the nLab if things are linked correctly. It is rather hard to find mention of these categories by Googling for such common words as “category” and “injection”.

    • CommentRowNumber7.
    • CommentAuthorTodd_Trimble
    • CommentTimeNov 5th 2013

    Okay, Rod, that sounds good to me.

    • CommentRowNumber8.
    • CommentAuthorTobyBartels
    • CommentTimeNov 25th 2013

    Was anything created?

    • CommentRowNumber9.
    • CommentAuthorRodMcGuire
    • CommentTimeSep 5th 2017

    I’ve finally made Inj. Comments should go to nForum:Inj